Assignment- Sampling Distributions and Estimation; Hypothesis Testing

1. In a simple random sample from a population of several hundred that's approximately normally distributed, the following data values were collected.

68, 79, 70, 98, 74, 79, 50, 102, 92, 96

Based on this information, the confidence level would be 90% that the population mean is somewhere between
A. 73.36 and 88.24.
B. 69.15 and 92.45.
C. 71.36 and 90.24.
D. 65.33 and 95.33.

2. What is the purpose of sampling?
A. To verify that the population is approximately normally distributed
B. To estimate a target parameter of the population
C. To create a point estimator of the population mean or proportion
D. To achieve a more accurate result than can be achieved by surveying the entire population

3. To schedule appointments better, the office manager for an ophthalmologist wants to estimate the average time that the doctor spends with each patient. A random sample of 49 is taken, and the sample mean is 20.3 minutes. Assume that the office manager knows from past experience that the standard deviation is 14 minutes. She finds that a 95% confidence interval is between 18.3 and 22.3 minutes. What is the point estimate of the population mean, and what is the confidence coefficient?
A. 20.3, 0.95
B. 20.3, 95%
C. 18.3, 0.95
D. 18.3, 95%

4. A researcher wants to carry out a hypothesis test involving the mean for a sample of n = 20. While the true value of the population standard deviation is unknown, the researcher is reasonably sure that the population is normally distributed. Given this information, which of the following statements would be correct?
A. The t-test should be used because α and μ are unknown.
B. The researcher should use the z-test because the population is assumed to be normally distributed.
C. The t-test should be used because the sample size is small.

5. Nondirectional assertions lead only to -tail tests.
A. right
B. two
C. one
D. left

6. In a criminal trial, a Type II error is made when a/an
A. guilty defendant is acquitted.
B. guilty defendant is convicted.
C. innocent person is acquitted.
D. innocent person is convicted.

7. A woman and her son are debating about the average length of a preacher's sermons on Sunday morning. Despite the mother's arguments, the son thinks that the sermons are more than twenty minutes. For one year, he has randomly selected 12 Sundays and found an average time of 26.42 minutes with a standard deviation of 6.69 minutes. Assuming that the population is normally distributed and using a 0.05 level of significance, he wishes to determine whether he is correct in thinking that the average length of sermons is more than 20 minutes. What is the test statistic?
A. -3.32
B. 3.32
C. 0.95
D. 6.69

8. Which of the following statements about hypothesis testing is false?
A. In both the one-tailed and two-tailed tests, the rejection region is one contiguous interval on the number line.
B. A Type I error is the chance that the researcher rejects the null hypothesis when in fact the null hypothesis is true.
C. The rejection region is always given in units of standard deviations from the mean.
D. The test will never confirm the null hypothesis, only fail to reject the null hypothesis.

9. Determine which of the following four population size and sample size combinations would not require the use of the finite population correction factor in calculating the standard error.
A. N = 2500; n = 75 B. N = 1500; n = 300 C. N = 150; n = 25
D. N = 15,000; n = 1,000

10. The power of a test is the probability of making a/an decision when the null hypothesis is
A. incorrect, false
B. correct, true
C. incorrect, true

11. For 1996, the U.S. Department of Agriculture estimated that American consumers would have eaten, on average, 2.6 pounds of cottage cheese throughout the course of that year. Based on a longitudinal study of 98 randomly selected people conducted during 1996, the National Center for Cottage Cheese Studies found an average cottage cheese consumption of 2.75 pounds and a standard deviation of s = 14 ounces. Given this information, which of the following statements would be correct concerning a two-tail test at the 0.05 level of significance?
A. We can conclude that the average cottage cheese consumption in America is actually 2.75 pounds per person per year.
B. We can conclude that we can't reject the claim that the average cottage cheese consumption in America is 2.6 pounds per person per year.
C. We can conclude that the average cottage cheese consumption in America is at least 0.705 pound more or less than 2.75 pounds per person per year.
D. We can conclude that the average cottage cheese consumption in America isn't 2.6 pounds per person per year.

12. If a teacher wants to test her belief that more than five students in college classes typically receive A as a grade, she'll perform -tail testing of a .
A. one, proportion
B. two, mean
C. one, mean
D. two, proportion

13. Because of the popularity of movies as an entertainment medium for adolescents, an entrepreneur plans to do a national study of the average cost of a movie ticket. If you assume that s = $0.50, what sample size would the entrepreneur have to take to be 95% confident that the estimate was within $0.25 of the true mean ticket prices?
A. 8
B. 4
C. 15
D. 16

14. If the level of significance (α) is 0.005 in a two-tail test, how large is the nonrejection region under the curve of the t distribution?
A. 0.005
B. 0.995
C. 0.9975
D. 0.050

15. A mortgage broker is offering home mortgages at a rate of 9.5%, but the broker is fearful that this value is higher than many others are charging. A sample of 40 mortgages filed in the county courthouse shows an average of 9.25% with a standard deviation of 8.61%. Does this sample indicate a smaller average? Use α
= 0.05 and assume a normally distributed population.
A. No, because the test statistic falls in the acceptance region.
B. Yes, because the sample mean of 9.25 is below 9.5.
C. No, because the test statistic is -1.85 and falls in the rejection region.

16. What is the rejection region for a two-tailed test when α = 0.05?
A. |z | > 1.96 B. |z | > 2.575 C. |z | > 1.645 D. z > 2.575

17. In the statement of a null hypothesis, you would likely find which of the following terms?
A. ≠
B. =
C. >
D. <

18. A portfolio manager was analyzing the price-earnings ratio for this year's performance. His boss said that the average price-earnings ratio was 20 for the many stocks that his firm had traded, but the portfolio manager felt that the figure was too high. He randomly selected a sample of 50 price-earnings ratios and found a mean of 18.17 and a standard deviation of 4.60. Assume that the population is normally distributed, and test at the 0.01 level of significance. Which of the following is the correct decision rule for the manager to use in this situation?
A. Because -2.81 falls in the rejection region, reject H0. At the 0.01 level, the sample data suggest that the average price- earnings ratio for the stocks is less than 20.
B. If z > 2.33, reject H0.
C. Because 2.81 is greater than 2.33, reject H0. At the 0.01 level, the sample data suggest that the average price-earnings ratio for the stocks is less than 20.
D. If t > 2.68 or if t < -2.68, reject H0.

19. Which of the following statements about p-value testing is true?
A. The p-value is the lowest significance level at which you should reject H0.
B. P-value testing uses a predetermined level of significance.
C. The p represents sample proportion.
D. P-value testing applies only to one-tail tests.

20. A human resources manager wants to determine a confidence interval estimate for the mean test score for the next office-skills test to be given to a group of job applicants. In the past, the test scores have been normally distributed with a mean of 74.2 and a standard deviation of 30.9. Determine a 95% confidence interval estimate if there are 30 applicants in the group.
A. 64.92 to 83.48
B. 13.64 to 134.76
C. 63.14 to 85.26
D. 68.72 to 79.68.